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Spite

In fair division problems, spite is a phenomenon that occurs when a player's value of an allocation decreases when one or more other players' valuation increases. Thus, other things being equal, a player exhibiting spite will prefer an allocation in which other players receive less than more.
In this language, spite is difficult to analyze because one has to assess two sets of preferences. For example, in the divide and choose method, a spiteful player would have to make a trade-off between depriving his opponent of cake, and getting more himself.
Within the field of social evolution, spite is used to describe those social behaviors that have a negative impact on both the actor and recipient. Spite can be favored by kin selection when: it leads to an indirect benefit to some third party that is sufficiently related to the actor; or when it is directed primarily at negatively related individuals. Negative relatedness occurs when two individuals are less related than average.